Introduction

MCMC (Markov Chain Monte Carlo) and MC Statistical Methods are very powerful statistical techniques for parameter estimation and related problems. They are particularly useful for the difficult nonlinear or non-Gaussian case. Using a large data set, these techniques can also be used to make inference on parameters, to integrate nuisance parameters, to evaluate functions numerically or to solve optimization problems.

Previous Work

We have applied these methods to several interesting problems: (J-R. Larocque)

1. Joint model order detection and DOA estimation in coloured noise
   Model order detection has always been a difficult problem in array signal processing w hen the noise is coloured. A novel reversible jump MCMC approach has been proposed to solve this problem (IEEE Trans Signal Processing, Feb., 2002). Download.
2. Tracking of multiple targets using arrays of sensors
   In this project, arrays of sensors are used to detect the number of targets and to jointly track their directions of arrival, using particle filters, or sequential Monte Carlo approaches. These methods approach real-time efficiency and show considerable advantages over previous techniques. A submission has been made to IEEE Trans. SP. Download.

Current Work

The following work is being done by William Ng.

Work is now in progress with the objective of using MCMC and sequential MC methods for restoration of signals using sensor arrays; i.e., we wish to extract a signal of interest from multiple interfering sources. This has been accomplished for the narrowband case, and work has been extended to the more difficult wideband case.

Details about these subjects can be downloaded from here.